On volumes of arithmetic line bundles
By Xinyi Yuan. Compositio Mathematica, 2008
49 citations recorded by the source corpus.
Abstract We show an arithmetic generalization of the recent work of Lazarsfeld–Mustaţǎ which uses Okounkov bodies to study linear series of line bundles. As applications, we derive a log-concavity inequality on volumes of arithmetic line bundles and an arithmetic Fujita approximation theorem for big line bundles.
Subfields: Applied Mathematics, Geometry and Topology
View Paper: https://www.semanticscholar.org/paper/7b47b167c80dc0da7f4dfbed7d41eb3f5e2fba87
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In Applied Mathematics
- M. Mustaţă
- Askold Khovanskii
- R. Lazarsfeld
- Kiumars Kaveh
- Chi Li
- Mattias Jonsson
- S. Boucksom
- Yuchen Liu
In Geometry and Topology
- Kiumars Kaveh
- Askold Khovanskii
- M. Mustaţă
- Chi Li
- R. Lazarsfeld
- Steven Dale Cutkosky
- Mattias Jonsson
- H. Blum
Citations in the corpus
- Newton-Okounkov bodies, semigroups of integral points, graded algebras and intersection theory (2009, methodology): “oducedaboutthe sametime inthe papers[Lazarsfeld-Mustata08]and[Kaveh-Khovanskii08a]. Recently the Newton-Okounkovbody (which Lazarsfeld-Mustatacall Okounkovbody) has been exploredand used in the papers[Yuan09], [Nystrom09], [Jow10] and [Boucksom-Chen09]. There is also the nice recent paper [Kuronya-L”
- Convex Bodies Associated to Linear Series (2008, background): “(17) Note added January, 2009: such arithmetic Okounkov bodies have been constructed by Yuan [44], who uses them to study the arithmetic volume function.”